Quantum Simulations of Classical Systems

ORAL

Abstract

Understanding the properties of classical systems on a lattice using numerical methods is, in general, a very hard problem. In this talk I will focus then on the quantum simulations of classical systems. That is, if we had a quantum computer, which properties could be obtained more efficiently on it than on a conventional one?. For this purpose, I will introduce a classical-to-quantum mapping that will allow us to understand classical and quantum annealing procedures as two independent paths on Quantum-Hamiltonian space. I present then the corresponding quantum algorithms to simulate classical systems and give convergence rates, determined by the adiabatic theorem, to assure successful simulation.

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Authors

  • Rolando Somma

    Los Alamos National Laboratory, LANL

  • Gerardo Ortiz

    Indiana University

  • Cristian Batista

    Los Alamos National Laboratory, Los Alamos National Lab, T-Division, Los Alamos National Laboratory, T-11, LANL

  • Emmanuel Knill

    National Institute of Standards and Technology, Boulder, Colorado 80305, USA, Mathematical and Computing Science Division, National Institute of Standards and Technology, Boulder, Colorado 80305, National Institute of Standards and Technology, NIST